73.10.10 problem 15.3

Internal problem ID [15305]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 15. General solutions to Homogeneous linear differential equations. Additional exercises page 294
Problem number : 15.3
Date solved : Tuesday, January 28, 2025 at 07:52:03 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 13

dsolve(x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_{1} x +c_{2} \right ) x^{2} \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 16

DSolve[x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 (c_2 x+c_1) \]